From now on, we fix \(G\)  as the simple real exceptional linear Lie group E7_q in atlas. This connected group is equal rank. That is, \(\mathfrak {h}_f=\mathfrak {t}_f\) . It has center \(\mathbb {Z}/2\mathbb {Z}\) . The Lie algebra \(\mathfrak {g}_0\)  of \(G\)  is denoted as EVI in [1]}.
Note that
\(-\mathop {\hbox{dim}}\nolimits \mathfrak {k}+\mathop {\hbox{dim}}\nolimits \mathfrak {p}=-69+64=-5.\) 
